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Shrinkage estimation of location parameters in a multivariate skew-normal distribution

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  • Tatsuya Kubokawa
  • William E. Strawderman
  • Ryota Yuasa

Abstract

This paper studies decision theoretic properties of Stein type shrinkage estimators in simultaneous estimation of location parameters in a multivariate skew-normal distribution with known skewness parameters under a quadratic loss. The benchmark estimator is the best location equivariant estimator which is minimax. A class of shrinkage estimators improving on the best location equivariant estimator is constructed when the dimension of the location parameters is larger than or equal to four. An empirical Bayes estimator is also derived, and motivated from the Bayesian procedure, we suggest a simple skew-adjusted shrinkage estimator and show its dominance property. The performances of these estimators are investigated by simulation.

Suggested Citation

  • Tatsuya Kubokawa & William E. Strawderman & Ryota Yuasa, 2020. "Shrinkage estimation of location parameters in a multivariate skew-normal distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(8), pages 2008-2024, April.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:8:p:2008-2024
    DOI: 10.1080/03610926.2019.1568481
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    Cited by:

    1. Yuanyuan Ju & Yan Yang & Mingxing Hu & Lin Dai & Liucang Wu, 2022. "Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models," Mathematics, MDPI, vol. 10(8), pages 1-19, April.

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